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Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
For decades, computational chemistry has been posited as one of the areas in which quantum computing would revolutionize. However, the algorithmic advantages that fault-tolerant quantum computers have for chemistry can be overwhelmed by…
Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…